Thinking and Reasoning

How do we solve a problem when we have never encountered a task of that kind previously?

Well Defined Problems and the Computational Approach

In theory, a program can be written to solve any well-defined problem, provided it has an unlimted amount of time available. A computer can easily play a perfect game of Scrabble because it has time to compute all possible means of laying the tiles on the board and can quickly check whether each letter string is a legal word, using its built-in dictionary.

A computer cannot play a perfect game of chess because there are too many possible positions and sequences arising in these games for it to compute and evaluate all of them. Such problems are described as being computationally intractable, meaning that they are beyond the computational power of contemporary machines.

Newell and Simon described problem solving as a search within a problem space.

A problem space is a set of possibilities generated by any well-defined problem.

A computational intractable problem is one with a very large problem space.

Newell and Simon suggested that both humans and computers needed intelligent methods to reduce the search space and called these heuristics. Heuristics cannot guarantee success but they can lead to effective solutions to problems that are otherwise computationally intractable. Once method is to work backwards from the desired solution to the current state, creating a subgoal.

People use heuristics to solve problems with large problem spaces. There are many heuristics that humans can use to solve difficult problems. But they will not necessarilty be applied consciously. Heuristics can operate in an intuitive or perceptual manner.

This comes from experience. This is a kind of insight, as potential solutions are perceived without any process of conscious reasoning. Heuristics can be explicit rules that can be taught to people to aid their problem solving.

For example, to solve an anagram, it is helpful to look for familiar letter strings. Say you have a 10 letter anagram but notice it contains an i, n and g. You could suppose that it is a word ending in ‘ing’. This might be wrong. But for the time being you have reduced a 10 letter anagram to one of 7 letters which is easier to solve. If the anagram is contained in a crossword clue you can try to determine the meaning of the solution word, which can help you to tell if this heuristic is likely to work.

Thinking Test

A bat and ball together cost $1.10. If the bat costs one dollar more than the ball, how much does the ball cost?

Well defined problems can be difficult because they have a large search space, like finding a good chess move. But they can also be hard for a different kind of reason: they may have a compelling but WRONG intuitive solution.

This is demonstrated in this test of thinking. The solution can easily be computed, but also have a competing and wrong and intuitive answer.

The correct answer can be deduced with some algebra.

bat + ball = 1.10 bat = 1 + ball

1 + ball + ball = 1.10

2ball = 0.10 ball = 0.05

But the incorrect answer comes directly to mind and people often give this without thinking. Some are consistently likely to make this kind of error, while others check their intuitions by reasoning.

Dual Process Theory

This is related to Dual Process Theory. The theory distinguishes between thought based on Type 1 processes (rapid and intuitive) and Type 2 processes (slow and reflective). We cannot rely on Type 1 when Type 2 is needed to solve a problem.

Dual Process Theory suggests that human cognition has two distinct types of processes: System 1 and System 2.

System 1

• Automatic: Functions without conscious thought.
• Fast: Makes quick judgments and decisions.
• Heuristic-based: Relies on mental shortcuts.
• Emotion-driven: May involve gut feelings or instincts.

System 2

• Controlled: Requires conscious thought and effort.
• Slow: Takes time to arrive at decisions.
• Analytic: Uses logical reasoning and analysis.
• Rational: Not as influenced by emotion.

Interaction

System 1 often provides initial judgments that System 2 can evaluate and modify. Sometimes System 2 is lazy and just goes along with the quick judgment from System 1. At other times, System 2 overrides or corrects the intuition of System 1, especially if it detects an error.

Key Takeaways

• System 1 and System 2 have different characteristics and serve different functions.
• Both systems interact to form our judgments and make decisions.
• Being aware of these systems can help in understanding human behavior and decision-making.

Reference

• Thinking and Reasoning: A Very Short Introduction by Jonathan St B. T. Evans